Critical thickness for high-remanent single-domain configurations in square ferromagnetic thin platelets

By means of three-dimensional micromagnetic finite element modeling, zero-field magnetization patterns of ferromagnetic thin film elements of square shape are simulated and energetically compared. The geometry of the sample (edge length $a,$ thickness $D)$ and its intrinsic material parameters (hardness $Q)$ are systematically varied. Based on the results the corresponding phase diagram is set up which identifies a quasihomogeneous single-domain phase (C, S, and flower states) and a vortex phase (Landau state). For the transition between the two phases a material- and edge-length-dependent critical film thickness is found. The numerical results can be confirmed qualitatively using a simple analytical model calculation.